Qualitative vs. quantitative differences / of kind vs. of degree
It’s not like the distinction is meaningless (in some sense liquid water certainly isn’t “just ice but warmer”) but most of the times in my life I recall having encountered it, it was abused or misapplied in one way or another:
(1) It seems to be very often (usually?) used to downplay some difference between A and B by saying “this is just a difference of degree, not a difference of kind” without explaining why one believes so or pointing out an example of an alternative state of the world in which a difference between A and B would be qualitative.
(2) It is often ignored that differences of degree can become differences of kind after crossing some threshold (probably most, if not all, cases of latter are like that). At some point ice stops just becoming warmer and melts, a rocket stops just accelerating and reaches escape velocity, and a neutron start stops just increasing in mass and collapses into a black hole.
(3) Whenever this distinction is being introduced, it should be clear what is meant by qualitative and quantitative difference in this particular domain of discourse, either with reference to some qualitativeness/quantitativeness criteria or by having sets of examples of both. For example, when comparing intelligence between species, one could make a case that we see a quantitative difference between ravens and new Caledonian crows but qualitative between birds and hookworms. We may not have a single, robust metric for comparing average intelligence between taxa but in this case we know it when we see it and we can reasonably expect other to see the distinction as well. (TL;DR it shouldn’t be based on gut feeling when gut feeling about what is being discussed is likely to differ between individuals)
Qualitative vs. quantitative differences / of kind vs. of degree
It’s not like the distinction is meaningless (in some sense liquid water certainly isn’t “just ice but warmer”) but most of the times in my life I recall having encountered it, it was abused or misapplied in one way or another:
(1) It seems to be very often (usually?) used to downplay some difference between A and B by saying “this is just a difference of degree, not a difference of kind” without explaining why one believes so or pointing out an example of an alternative state of the world in which a difference between A and B would be qualitative.
(2) It is often ignored that differences of degree can become differences of kind after crossing some threshold (probably most, if not all, cases of latter are like that). At some point ice stops just becoming warmer and melts, a rocket stops just accelerating and reaches escape velocity, and a neutron start stops just increasing in mass and collapses into a black hole.
(3) Whenever this distinction is being introduced, it should be clear what is meant by qualitative and quantitative difference in this particular domain of discourse, either with reference to some qualitativeness/quantitativeness criteria or by having sets of examples of both. For example, when comparing intelligence between species, one could make a case that we see a quantitative difference between ravens and new Caledonian crows but qualitative between birds and hookworms. We may not have a single, robust metric for comparing average intelligence between taxa but in this case we know it when we see it and we can reasonably expect other to see the distinction as well. (TL;DR it shouldn’t be based on gut feeling when gut feeling about what is being discussed is likely to differ between individuals)